Condensed Matter Seminars

Because of potential relevance to topological quantum information processing, we introduce and study the self-dual family of representations of the braid group. Self-dual representations are physically motivated by strong-coupling/weak-coupling dualities in clock models and include as special cases the Majorana and Gaussian (metaplectic) representations. To show that self-dual representations admit a particle interpretation, we introduce and describe in second quantization a family of particle species with (p=2,3,dots) exclusion and ( heta=2pi/p) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally associated to the parafermionic zero-energy modes potentially realizable in mesoscopic arrays of fractional topological insulators. Self-dual representations are local combinations of either parafermions or Fock parafermions, an important requisite for the potential physical implementation of (semi-)topologically protected quantum logic gates. The second-quantization description of Fock parafermions entails the concept of Fock algebra, i.e., a Fock space endowed with a statistical multiplication that captures and logically correlates these anyons' exclusion and exchange statistics. As a consequence, normal-ordering remains a well-defined operation.